Liouvillian Approach to the Integer Quantum Hall Effect Transition

We present a novel approach to the localization-delocalization transition in the integer quantum Hall effect. The Hamiltonian projected onto the lowest Landau level can be written in terms of the projected density operators alone. This and the closed set of commutation relations between the projected densities leads to simple equations for the time evolution of the density operators. These equations can be used to map the problem of calculating the disorder averaged and energetically unconstrained density-density correlation function to the problem of calculating the one-particle density of states of a dynamical system with a novel action. At the self-consistent mean-field level, this approach yields normal diffusion and a finite longitudinal conductivity. While we have not been able to go beyond the saddle point approximation analytically, we show numerically that the critical localization exponent can be extracted from the energetically integrated correlation function yielding $\nu=2.33 \pm 0.05$ in excellent agreement with previous finite-size scaling studies.Comment: 9 pages, submitted to PR

Mott insulators in strong electric fields

Recent experiments on ultracold atomic gases in an optical lattice potential have produced a Mott insulating state of Rb atoms. This state is stable to a small applied potential gradient (an `electric' field), but a resonant response was observed when the potential energy drop per lattice spacing (E), was close to the repulsive interaction energy (U) between two atoms in the same lattice potential well. We identify all states which are resonantly coupled to the Mott insulator for E close to U via an infinitesimal tunneling amplitude between neighboring potential wells. The strong correlation between these states is described by an effective Hamiltonian for the resonant subspace. This Hamiltonian exhibits quantum phase transitions associated with an Ising density wave order, and with the appearance of superfluidity in the directions transverse to the electric field. We suggest that the observed resonant response is related to these transitions, and propose experiments to directly detect the order parameters. The generalizations to electric fields applied in different directions, and to a variety of lattices, should allow study of numerous other correlated quantum phases.Comment: 17 pages, 14 figures; (v2) minor additions and new reference

Mott Transition in An Anyon Gas

We introduce and analyze a lattice model of anyons in a periodic potential and an external magnetic field which exhibits a transition from a Mott insulator to a quantum Hall fluid. The transition is characterized by the anyon statistics, $\alpha$, which can vary between Fermions, $\alpha=0$, and Bosons, $\alpha=1$. For bosons the transition is in the universality class of the classical three-dimensional XY model. Near the Fermion limit, the transition is described by a massless $2+1$ Dirac theory coupled to a Chern-Simons gauge field. Analytic calculations perturbative in $\alpha$, and also a large N-expansion, show that due to gauge fluctuations, the critical properties of the transition are dependent on the anyon statistics. Comparison with previous calcualations at and near the Boson limit, strongly suggest that our lattice model exhibits a fixed line of critical points, with universal critical properties which vary continuosly and monotonically as one passes from Fermions to Bosons. Possible relevance to experiments on the transitions between plateaus in the fractional quantum Hall effect and the magnetic field-tuned superconductor-insulator transition are briefly discussed.Comment: text and figures in Latex, 41 pages, UBCTP-92-28, CTP\#215

Critical Currents of Ideal Quantum Hall Superfluids

Filling factor $\nu=1$ bilayer electron systems in the quantum Hall regime have an excitonic-condensate superfluid ground state when the layer separation $d$ is less than a critical value $d_c$. On a quantum Hall plateau current injected and removed through one of the two layers drives a dissipationless edge current that carries parallel currents, and a dissipationless bulk supercurrent that carries opposing currents in the two layers. In this paper we discuss the theory of finite supercurrent bilayer states, both in the presence and in the absence of symmetry breaking inter-layer hybridization. Solutions to the microscopic mean-field equations exist at all condensate phase winding rates for zero and sufficiently weak hybridization strengths. We find, however, that collective instabilities occur when the supercurrent exceeds a critical value determined primarily by a competition between direct and exchange inter-layer Coulomb interactions. The critical current is estimated using a local stability criterion and varies as $(d_c-d)^{1/2}$ when $d$ approaches $d_c$ from below. For large inter-layer hybridization, we find that the critical current is limited by a soliton instability of microscopic origin.Comment: 18 RevTeX pgs, 21 eps figure

Schwinger boson theory of anisotropic ferromagnetic ultrathin films

Ferromagnetic thin films with magnetic single-ion anisotropies are studied within the framework of Schwinger bosonization of a quantum Heisenberg model. Two alternative bosonizations are discussed. We show that qualitatively correct results are obtained even at the mean-field level of the theory, similar to Schwinger boson results for other magnetic systems. In particular, the Mermin-Wagner theorem is satisfied: a spontaneous magnetization at finite temperatures is not found if the ground state of the anisotropic system exhibits a continuous degeneracy. We calculate the magnetization and effective anisotropies as functions of exchange interaction, magnetic anisotropies, external magnetic field, and temperature for arbitrary values of the spin quantum number. Magnetic reorientation transitions and effective anisotropies are discussed. The results obtained by Schwinger boson mean-field theory are compared with the many-body Green's function technique.Comment: 14 pages, including 7 EPS figures, minor changes, final version as publishe